The former prime minister is facing criticism for his intervention in the campaign as opinion polls show Labour may only be able to form a government with SNP support.
Sir John said Ed Miliband would have "a daily dose of political blackmail" if he had to do deals with the Scottish nationalists and that the party would push him "slowly but surely ... further to the left".
He warned: "They will ask for the impossible and create merry hell if it is denied.
"The nightmare of a broken United Kingdom has not gone away. The separation debate is not over. The SNP is determined to prise apart the United Kingdom."
But Christian Labour candidate for Stockton North, Alex Cunningham, told Premier's News Hour that Sir John's warning was 'absolute nonsense'.
He said Labour was fighting for a majority and would not enter into any deal with the SNP.
"There won't be any Labour deal with the SNP," he stressed, "We don't need the SNP, what we actually need is a Labour government with Labour policies, that can drive the future that we need for our country."
He said Labour would talk to all political parties following the election and would be able to "operate as a minority government".
"The Tories are playing a very dangerous game as far as Scotland is concerned.
"I don't know whether they're actually trying to persuade Tory voters to vote for the SNP."
But Murdo Fraser, a Christian and Conservative Member of Scottish Parliament, told Premier's News Hour: "We saw Nicola Sturgeon just last week in the challenger debate saying to Ed Miliband, I'll put you into government Ed if you shift to the left and do as I say.
"We face this very worrying prospect of a Labour government being elected and being dragged off to the left."
SNP leader Nicola Sturgeon said Sir John's comments were "silly, over the top" and "an affront to democracy".
She added: "My message to John Major is Scotland's voice deserves to be heard in whatever way the Scottish people choose, and voting SNP means Scotland's voice will be heard more loudly and strongly at Westminster than it has ever been heard before."